Another important question to which we do not have an
unambiguous answer is: “do we live in a spatially flat or in a spatially curved
universe?” When CMB data from the Planck mission [1]}
are combined with those from the South Pole Observatory (ACT),
and assuming a FLRW geometry,
one obtains a Universe which is consistent with flat spatial sections,
i.e.
when LSS BAO data are also included one obtains
\(\Omega _\kappa =-\kappa /H_0^2 = 0.001\pm 0.002\) ,
where \(H_0\)  is the expansion rate of the Universe today
and \(\kappa \)  Gauss' curvature of the spatial sections.
However, Planck's data alone
show evidence for a positively
curved universe (\(\kappa >0\) ),
and depending on the type of analysis used, one obtains
\(\Omega _\kappa = -0.044{+0.018\atop -0.015}\; (3.4\sigma )\) 
when baseline Plik likelihood is used
and \(\Omega _\kappa = -0.035 {+0.018\atop -0.013}\; (\gtrsim 2\sigma )\) 
when CamCode likelihood analysis is used.
At this moment it is unclear whether that is yet another anomaly,
or a calibration problem.
While the Planck collaboration analyses are based on the whole sky data,
the ACT covers a fraction of the sky, possibly indicating a directional dependence in spatial curvature.
A definite answer of this intriguing question will have to wait for
EUCLID and SKAO, whose observations will break
Planck data degeneracies with regard
to \(\Omega _\kappa \)  and allow for a highly accurate measurement
of spatial curvature, with an error of the order
\(\Delta \Omega _\kappa \sim 10^{-3}\)  [2]}, [3]}.
